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A114443
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Indices of 4-almost prime pentagonal numbers.
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0
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12, 15, 16, 19, 24, 33, 36, 39, 45, 47, 52, 55, 56, 57, 60, 68, 70, 77, 82, 83, 84, 88, 90, 95, 102, 103, 104, 105, 110, 111, 114, 119, 124, 127, 138, 140, 142, 143, 145, 150, 153, 156, 163, 169, 172, 177, 179, 182, 183, 191, 196, 198
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| P(2) = 5 is the only prime pentagonal number, all other factor as P(k) = (k/2)*(3*k-1) or k*((3*k-1)/2) and thus have at least 2 prime factors. P(k) is semiprime iff [k prime and (3*k-1)/2 prime] or [k/2 prime and 3*k-1 prime].
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LINKS
| Eric Weisstein's World of Mathematics, Pentagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
| {a(n)} = {k such that A001222(A000326(k)) = 4}. {a(n)} = {k such that k*(3*k-1)/2 has exactly 4 prime factors}. {a(n)} = {k such that A000326(k) is an element of A014613}.
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EXAMPLE
| a(1) = 12 because P(12) = PentagonalNumber(12) = 12*(3*12-1)/2 = 210 = 2 * 3 * 5 * 7 is a 4-almost prime In fact the primorial 4#).
a(3) = 16 because P(16) = 16*(3*16-1)/2 = 376 = 2^3 * 47 is a 4-almost
prime (the prime factors need not be distinct).
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CROSSREFS
| Cf. A000326, A001222, A014613, A115709.
Sequence in context: A139310 A180575 A115402 * A188766 A153047 A164782
Adjacent sequences: A114440 A114441 A114442 * A114444 A114445 A114446
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 14 2006
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EXTENSIONS
| 82 inserted by R. J. Mathar, Dec 22 2010
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